+130071 Due to symmetry the x coordinate of the vertex = 5
The points (3,0) (7,0) and (2, - 5) are on the graph
And we have this form
y = ax^2 + bx + c
The x coordinate of the vertex =
-b / (2a) = 5
-b = 10a
b = -10a
So we have that using (3,0)
0 = a(3)^2 - 10a(3) + c
0 = 9a - 30a + c
0 = - 21a + c
-c = -21a
c = 21a
And using (2, -5)
-5 = a(2)^2 - 10a(2) + 21a
-5 = 4a - 20a + 21a
-5 = 5a
a = -1
And b = -10(-1) = 10
And c = 21(-1) = -21
So our function is :
y = -1x^2 + 10x - 21
Here;s the graph : https://www.desmos.com/calculator/u2qnb8dswx
